Description
Probability-Statistics seminar
Speaker: Dr. Dootika Vats
NSF Postdoctoral Fellow
Department of Statistics
University of Warwick
Venue: Ramanujan Hall
Time: 2:30 p.m. -- 3:30 p.m.
Date: 28th September, 2018
Title*: *Lugsail lag windows and their application to Markov chain Monte
Carlo
Abstract*: *
Lag windows are commonly used in the time series, steady state simulation,
and Markov chain Monte Carlo (MCMC) literature to estimate the long range
variances of ergodic averages. We propose a new lugsail lag window
specifically designed for improved finite sample performance. We use this
lag window for batch means and spectral variance estimators in MCMC
simulations to obtain strongly consistent estimators that are biased from
above in finite samples and asymptotically unbiased. This quality is
particularly useful when calculating effective sample size and using
sequential stopping rules where they help avoid premature termination.
Further, we calculate the bias and variance of lugsail estimators and
demonstrate that there is little loss compared to other estimators. We also
show mean square consistency of these estimators under weak conditions. Our
results hold for processes that satisfy a strong invariance principle,
providing a wide range of practical applications of the lag windows outside
of MCMC. Finally, we study the finite sample properties of lugsail
estimators in various examples.